\[ y'(x)=\frac {x \left (\text {$\_$F1}\left (y(x)^2-2 x\right )+\frac {1}{x}\right )}{\sqrt {y(x)^2}} \] ✓ Mathematica : cpu = 0.634202 (sec), leaf count = 103
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {K[2]^2}}{\text {$\_$F1}\left (K[2]^2-2 x\right )}-\int _1^x\frac {2 K[2] \text {$\_$F1}'\left (K[2]^2-2 K[1]\right )}{\left (\text {$\_$F1}\left (K[2]^2-2 K[1]\right )\right ){}^2}dK[1]\right )dK[2]+\int _1^x\left (-K[1]-\frac {1}{\text {$\_$F1}\left (y(x)^2-2 K[1]\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.318 (sec), leaf count = 65
\[\left \{y \left (x \right ) = \sqrt {2 x +2 \RootOf \left (x^{2}+4 c_{1}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )\right )}, y \left (x \right ) = -\sqrt {2 x +2 \RootOf \left (x^{2}+4 c_{1}-2 \left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_F1} \left (2 \textit {\_a} \right )}d \textit {\_a} \right )\right )}\right \}\]